Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
Sketch the derivative of the graph shown here
![**Challenge #1: Sketch the DERIVATIVE of the graph shown here.**
The image depicts a graph with a red line on a coordinate plane. This line passes through the origin (0,0) and has a positive slope. Specifically, the line appears to follow the equation \( y = x \), as it rises one unit for every unit it moves to the right.
**Explanation of Graph:**
- **Axes:** The graph has standard x and y axes, with the origin at coordinate (0,0). Both axes are marked at intervals of 2, ranging from -8 to 8 on the x-axis and -4 to 4 on the y-axis.
- **Line:** The red line in the graph has a uniformly positive slope, indicating a constant rate of change.
- **Derivative:** The slope of the line is constant, suggesting that its derivative is also constant. Since this line appears to be \( y = x \), the derivative \( y' \) is 1.
Therefore, the derivative of this graph is a horizontal line at \( y = 1 \) across the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f5b0569-83e9-4f3d-93a8-6d46166ffdc9%2Ffb4ce559-c27c-4384-9600-3039cf1d4413%2F6g2r5_processed.png&w=3840&q=75)
Transcribed Image Text:**Challenge #1: Sketch the DERIVATIVE of the graph shown here.**
The image depicts a graph with a red line on a coordinate plane. This line passes through the origin (0,0) and has a positive slope. Specifically, the line appears to follow the equation \( y = x \), as it rises one unit for every unit it moves to the right.
**Explanation of Graph:**
- **Axes:** The graph has standard x and y axes, with the origin at coordinate (0,0). Both axes are marked at intervals of 2, ranging from -8 to 8 on the x-axis and -4 to 4 on the y-axis.
- **Line:** The red line in the graph has a uniformly positive slope, indicating a constant rate of change.
- **Derivative:** The slope of the line is constant, suggesting that its derivative is also constant. Since this line appears to be \( y = x \), the derivative \( y' \) is 1.
Therefore, the derivative of this graph is a horizontal line at \( y = 1 \) across the graph.
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